I'm a US citizen living in Buenos Aires (I have a DNI as a resident)

Ben, you should first prepare the relevant documents: your passport and copy of its data page, a completed application form with a passport-style photo attached, your DNI in Argentina, and proof of transportation and accommodation arrangements.
And then submit the application to the embassy of PRC to apply for it.

Thank you for your reply.
I'm a businessman and would like a 10 year visa with multiple entries, what's the best way to go about getting one?
Thank you again.
Ben

Ben, you can just prepare the above-mentioned documents and state that you want to apply for the 10-year one on the application form. After, apply for it.